Finite Group Databasebeta

← #28345202

Subgroups — #28345202

Order 13696.

492 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812117C211yesmaximal, characteristic, complemented
2C2×#16812115C211yesmaximal, characteristic, complemented
3#20293174C211yesmaximal, characteristic
4#20292703C211yesmaximal, characteristic, complemented
5#20292702C211yesmaximal, characteristic, complemented
6#20292700C211yesmaximal, characteristic, complemented
7#20292699C211yesmaximal, characteristic, complemented
8#20292697C211yesmaximal, characteristic, complemented
9C8×C22⋊D107C211yesmaximal, characteristic, complemented
10(C22⋊D107)⋊C8C211yesmaximal, characteristic, complemented
11C4⋊C8×D107C211yesmaximal, characteristic, complemented
12#20292592C211yesmaximal, characteristic, complemented
13#20292592C211yesmaximal, characteristic, complemented
14#20292579C211yesmaximal, characteristic, complemented
15#435×C107C211yesmaximal, characteristic, complemented
16C2×#13133818C2211yescharacteristic
17C2×#13133818C2211yescharacteristic
18#16812117—24no—
19#16812115—24no—
20C2×#13133802C2211yescharacteristic
21C2×#13133801C2211yescharacteristic
22C2×#13133801C2211yescharacteristic
23C2×#13133801C2211yescharacteristic
24C2×#13133801C2211yescharacteristic
25C22×C107⋊C8C2211yescharacteristic
26C2×C8×D107C2211yescharacteristic
27C2×C8×D107C2211yescharacteristic
28C2×C8×D107C2211yescharacteristic
29C2×C8×D107C2211yescharacteristic
30#16812108C411yescharacteristic
31#16812105C411yescharacteristic
32#16812095C411yescharacteristic
33#16812095C411yescharacteristic
34#16812084C411yescharacteristic
35#16812082C411yescharacteristic
36#16812082C411yescharacteristic
37#16812080C411yescharacteristic
38C4×D428C2211yescharacteristic
39C4×C22⋊D107C2211yescharacteristic
40C4×C22⋊D107C2211yescharacteristic
41C42×D107C2211yescharacteristic
42C4⋊(C107⋊C8)C2211yescharacteristic
43Dic107⋊C8C2211yescharacteristic
44Dic107⋊C8C2211yescharacteristic
45C22⋊(C107⋊C8)C2211yescharacteristic
46C22⋊(C107⋊C8)C2211yescharacteristic
47(C2×D107)⋊C8C2211yescharacteristic
48(C2×D107)⋊C8C2211yescharacteristic
49(C2×D107)⋊C8C2211yescharacteristic
50(C2×D107)⋊C8C2211yescharacteristic
51#16812020C2211yescharacteristic
52C8×Dic107C2211yescharacteristic
53C8×Dic107C2211yescharacteristic
54C2×M16×C107C2211yescharacteristic
55C22×C8×C107C2211yescharacteristic
56C4×D4×C107C2211yescharacteristic
57C4⋊C8×C107C2211yescharacteristic
58C22⋊C8×C107C2211yescharacteristic
59C22⋊C8×C107C2211yescharacteristic
60#97×C107C2211yescharacteristic
61#13133818—22no—
62#13133818—22no—
63#13133818—22no—
64#13133818—22no—
65C2×Dic214C2×C411yescharacteristic
66C2×Dic214C2×C411yescharacteristic
67C2×D428C2×C411yescharacteristic
68C2×D428C2×C411yescharacteristic
69C2×D428C2×C411yescharacteristic
70C2×C22⋊D107C2×C411yescharacteristic
71C2×C22⋊D107C2×C411yescharacteristic
72C2×C22⋊D107C2×C411yescharacteristic
73C2×C22⋊D107C2×C411yescharacteristic
74C2×C22⋊D107C2×C411yescharacteristic
75C2×C22⋊D107C2×C411yescharacteristic
76C2×C4×D107C2×C411yescharacteristic
77C2×C4×D107C2×C411yescharacteristic
78C2×C4×D107C2311yescharacteristic
79C2×C4×D107C2311yescharacteristic
80C2×C4×D107C2311yescharacteristic
81#13133802—22no—
82#13133801—22no—
83#13133801—22no—
84#13133801—22no—
85#13133801D414yescomplemented
86C2×C107⋊C8—22no—
87C2×C107⋊C8C2311yescharacteristic
88C2×C107⋊C8C2311yescharacteristic
89C2×C107⋊C8C2311yescharacteristic
90C2×C107⋊C8C2311yescharacteristic
91C8×D107—22no—
92C8×D107—22no—
93C8×D107—22no—
94C8×D107—22no—
95C4⋊Dic107C2×C411yescharacteristic
96Dic107⋊C4C2×C411yescharacteristic
97Dic107⋊C4C2×C411yescharacteristic
98C22⋊Dic107C2×C411yescharacteristic
99C22⋊Dic107C2×C411yescharacteristic
100(C2×D107)⋊C4C2×C411yescharacteristic
101(C2×D107)⋊C4C2×C411yescharacteristic
102(C2×D107)⋊C4C2×C411yescharacteristic
103(C2×D107)⋊C4C2×C411yescharacteristic
104C4×Dic107C2×C411yescharacteristic
105C4×Dic107C2×C411yescharacteristic
106C4×Dic107C2311yescharacteristic
107C2×D4×C107C2×C411yescharacteristic
108C22×C4×C107C2311yescharacteristic
109C22×C4×C107C2311yescharacteristic
110M16×C107—22no—
111C2×C8×C107—22no—
112C2×C8×C107C2311yescharacteristic
113C2×C8×C107C2311yescharacteristic
114C2×C8×C107C2311yescharacteristic
115C2×C8×C107C2311yescharacteristic
116C4⋊C4×C107C2×C411yescharacteristic
117C22⋊C4×C107C2×C411yescharacteristic
118C22⋊C4×C107C2×C411yescharacteristic
119C42×C107C2311yescharacteristic
120C23×C107C22×C411yescharacteristic
121C23×C107C22×C411yescharacteristic
122C22×D107C22×C411yescharacteristic
123C22×D107C22×C411yescharacteristic
124C22×D107C22×C411yescharacteristic
125D4×C107—41no—
126C2×C4×C107—21no—
127C2×C4×C107—21no—
128C2×C4×C107—21no—
129C2×C4×C107—21no—
130C2×C4×C107C22×C411yescharacteristic
131C2×C4×C107C22×C411yescharacteristic
132C2×C4×C107C22×C411yescharacteristic
133C2×C4×C107C22×C411yescharacteristic
134C2×C4×C107C2411yescharacteristic
135C22⋊D107—22no—
136C22⋊D107—22no—
137C22⋊D107—22no—
138C22⋊D107—22no—
139C22⋊D107—22no—
140C22⋊D107—22no—
141C2×Dic107C22×C411yescharacteristic
142C2×Dic107C22×C411yescharacteristic
143C2×Dic107C22×C411yescharacteristic
144C2×Dic107C22×C411yescharacteristic
145C2×Dic107C22×C411yescharacteristic
146D428—22no—
147D428—22no—
148D428—41no—
149C4×D107—21no—
150C4×D107—21no—
151C4×D107—21no—
152C4×D107—21no—
153C4×D107—22no—
154C4×D107—41no—
155C4×D107C2×D412yes—
156C4×D107#4112yes—
157Dic214—22no—
158Dic214—22no—
159C8×C107—21no—
160C8×C107—21no—
161C8×C107—21no—
162C8×C107C2×D412yes—
163C107⋊C8—21no—
164C107⋊C8—21no—
165C107⋊C8—21no—
166C107⋊C8C2×D412yes—
167C22×C107—21no—
168C22×C107—21no—
169C22×C107—21no—
170C22×C107—21no—
171C22×C107—21no—
172C22×C107—21no—
173C22×C107C23×C411yescharacteristic
174C2×D107—21no—
175C2×D107—21no—
176C2×D107—21no—
177C2×D107—21no—
178C2×D107—21no—
179C2×D107—21no—
180C2×D107—21no—
181C2×D107—21no—
182C2×D107C4×D412yes—
183C4×C107—21no—
184C4×C107—21no—
185C4×C107—21no—
186C4×C107—21no—
187C4×C107C22×D411yescharacteristic
188C4×C107C2×#4111yescharacteristic
189Dic107—21no—
190Dic107—21no—
191Dic107—21no—
192Dic107C4×D412yes—
193Dic107#13112yescomplemented
194C2×C107—41no—
195C2×C107—41no—
196C2×C107C2×C4×D411yescharacteristic
197C2×C107C2×#13111yescharacteristic
198C2×C107#56811yescharacteristic
199D107—22no—
200D107—41no—
201D107—41no—
202#2935—1071nomaximal, Sylow
203C107#293511yescharacteristic, complemented, Sylow
204C2×#131—1071no—
205C2×#131—1071no—
206#532—1071no—
207#436—1071no—
208#436—1071no—
209#435—1071no—
210#435—1071no—
211#435—1071no—
212#435D10711yescharacteristic, complemented
213C8×D4—1071no—
214C8×D4—1071no—
215C2×C4⋊C8—1071no—
216#408—1071no—
217#408—1071no—
218C4×M16—1071no—
219C2×#41—1071no—
220C2×#41—1071no—
221#131—2144no—
222#131—2144no—
223C2×M16—1071no—
224C2×M16—1071no—
225C2×M16—1071no—
226C2×M16—1071no—
227C2×M16—1071no—
228C2×M16C2×D10711yescharacteristic
229C22×C8—1071no—
230C22×C8—1071no—
231C22×C8—1071no—
232C22×C8—1071no—
233C22×C8—1071no—
234C22×C8C2×D10711yescharacteristic
235C4⋊Q8—1071no—
236#127—1071no—
237#124—1071no—
238#124—1071no—
239#121—1071no—
240#121—1071no—
241#121—1071no—
242#121—1071no—
243C4×D4—1071no—
244C4×D4—1071no—
245C4×D4—1071no—
246C4×D4C2×D10711yescharacteristic
247C2×C42—1071no—
248C4⋊C8—1071no—
249C4⋊C8—1071no—
250C4⋊C8—1071no—
251C4⋊C8C2×D10711yescharacteristic
252C22⋊C8—1071no—
253C22⋊C8—1071no—
254C22⋊C8—1071no—
255C22⋊C8—1071no—
256C22⋊C8—1071no—
257C22⋊C8—1071no—
258C22⋊C8C2×D10711yescharacteristic
259C22⋊C8C2×D10711yescharacteristic
260#97—1071no—
261#97C2×D10711yescharacteristic
262C4×C8—1071no—
263C4×C8—1071no—
264#41—2142no—
265#41—2142no—
266#41—2142no—
267#41—2142no—
268C2×Q8—1071no—
269C2×Q8—1071no—
270C2×D4—1071no—
271C2×D4—1071no—
272C2×D4—1071no—
273C2×D4—1071no—
274C2×D4—1071no—
275C2×D4—1071no—
276C2×D4—1071no—
277C2×D4—1071no—
278C2×D4—1071no—
279C2×D4C4×D10711yescharacteristic
280C22×C4—1071no—
281C22×C4—1071no—
282C22×C4—1071no—
283C22×C4—1071no—
284C22×C4—1071no—
285C22×C4C22×D10711yescharacteristic
286C22×C4C22×D10711yescharacteristic
287M16—22no—
288M16—1074no—
289M16—2142no—
290M16—2142no—
291M16—2142no—
292M16—2142no—
293C2×C8—22no—
294C2×C8—1071no—
295C2×C8—1071no—
296C2×C8—1071no—
297C2×C8—1071no—
298C2×C8—2142no—
299C2×C8—2142no—
300C2×C8—2142no—
301C2×C8—2142no—
302C2×C8—2142no—
303C2×C8C22×D10711yescharacteristic
304C2×C8C22×D10711yescharacteristic
305C2×C8C22×D10711yescharacteristic
306C2×C8C22×D10711yescharacteristic
307C4⋊C4—1071no—
308C4⋊C4—1071no—
309C4⋊C4—1071no—
310C4⋊C4C4×D10711yescharacteristic
311C22⋊C4—1071no—
312C22⋊C4—1071no—
313C22⋊C4—1071no—
314C22⋊C4—1071no—
315C22⋊C4—1071no—
316C22⋊C4—1071no—
317C22⋊C4C4×D10711yescharacteristic
318C22⋊C4C4×D10711yescharacteristic
319C42—1071no—
320C42—1071no—
321C42—1071no—
322C42C22×D10711yescharacteristic
323C23—1071no—
324C23—1071no—
325C23—1071no—
326C23C2×C4×D10711yescharacteristic
327C23C2×C4×D10711yescharacteristic
328Q8—2142no—
329Q8—2142no—
330D4—41no—
331D4—4281no—
332D4—2142no—
333D4—2142no—
334D4—2142no—
335D4—2142no—
336D4—2142no—
337D4—2142no—
338D4—2142no—
339D4—2142no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—1071no—
345C2×C4—1071no—
346C2×C4—1072no—
347C2×C4—1072no—
348C2×C4—1071no—
349C2×C4—1071no—
350C2×C4—1071no—
351C2×C4—4281no—
352C2×C4—2142no—
353C2×C4—2141no—
354C2×C4—2141no—
355C2×C4—2141no—
356C2×C4—2141no—
357C2×C4C2×C4×D10711yescharacteristic
358C2×C4C2×C4×D10711yescharacteristic
359C2×C4C2×C4×D10711yescharacteristic
360C2×C4C2×C4×D10711yescharacteristic
361C2×C4C23×D10711yescharacteristic
362C8—21no—
363C8—21no—
364C8—21no—
365C8—1072no—
366C8—2141no—
367C8—2141no—
368C8—2141no—
369C8D4×D10712yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—1072no—
377C22—2141no—
378C22—2141no—
379C22—2141no—
380C22—2141no—
381C22—2141no—
382C22—2141no—
383C22—2141no—
384C22—2141no—
385C22C22×C4×D10711yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—1072no—
391C4—1072no—
392C4—2141no—
393C4—2141no—
394C4—2141no—
395C4C2×D4×D10711yescharacteristic
396C4#41×D10711yescharacteristic
397C2—41no—
398C2—41no—
399C2—4281no—
400C2—4281no—
401C2—2142no—
402C2C4×D4×D10711yescharacteristic
403C2#131×D10711yescharacteristic
404C2#2029339311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D107
commutator, socleC22×C107C23×C4
Fitting#435×C107C2
prime radical#20293174C2
cosocleC2×C4×C107C24
hypercenter#435D107
hypocenterC107#2935
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ #435

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16812117C2semidirect
2. C2×#16812115C2semidirect
4. #20292703C2semidirect
5. #20292702C2semidirect
6. #20292700C2semidirect
7. #20292699C2semidirect
8. #20292697C2semidirect
9. C8×C22⋊D107C2semidirect
10. (C22⋊D107)⋊C8C2semidirect
11. C4⋊C8×D107C2semidirect
12. #20292592C2semidirect
13. #20292592C2semidirect
14. #20292579C2semidirect
15. #435×C107C2semidirect
85. #13133801D4semidirect
193. Dic107#131semidirect
203. C107#2935semidirect
212. #435D107semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168121172
C2×#168121152
#202931742
#202927032
#202927022
#202927002
#202926992
#202926972
C8×C22⋊D1072
(C22⋊D107)⋊C82
C4⋊C8×D1072
#202925922
#202925792
#435×C1072
#2935107